planets are part of the multiplayer campain, named planetwars. they are useless to own, impoortant for the faction though (in you case the greens). the gouvernment and the owner can waste ressources on the planet to build stuff, which benefits everyone in your faction. owning it gives you nothing special.

planetswars is actually not played, at a dead point.

ow. forgot: you might be able to get one when you are in the team, which fights for the planet in a planetwars battle (PW server only) and your team win. the winning team gets influence points for the faction they plan, the faction with the most influence (maybe even 100% needed nowadays) wins the planet. one of the players of that faction is selected to own it then. this often is someone who was impressive useless during the battle. but thats another topic.